Evolution of cooperation with asymmetric social interactions



Humans have a remarkable, but not pervasive, tendency towards selflessness. This behavior reflects a classic puzzle in evolutionary theory: when and why would individuals give up their selfish interests to help strangers? The population structure is known to catalyze cooperation because it enables local reciprocity – I help you and you help me. But this explanation assumes two-way social interactions, while human interactions are often one-way: one individual has the opportunity to altruistically contribute to another, but not the other way around. Here we find a surprising result, namely that directionality can actually facilitate cooperation. We study this effect theoretically and also in empirical social networks. We suggest several practical implications, including how to change the directions of social interactions to promote cooperation.


How cooperation emerges in human societies is both an evolutionary puzzle and a practical problem with tangible implications for the health of society. Population structure has long been recognized as a catalyst for cooperation because local interactions facilitate reciprocity. Analysis of population structure generally involves two-way social interactions. But human social interactions are often unidirectional – where one individual has the opportunity to altruistically contribute to another, but not the other way around – due to organizational hierarchies, social stratification, popularity effects, and endogenous mechanisms of change. network growth. Here, we expand the theory of cooperation in structured populations to account for one-way and two-way social interactions. Even though one-way interactions remove the possibility of reciprocity, we find that cooperation can nonetheless be fostered in directed social networks and that cooperation is proven to be maximized for networks with an intermediate proportion of one-way interactions, as observed in many cases. many empirical contexts. We also identify two simple structural patterns that allow efficient modification of the directions of interaction to promote order-of-magnitude cooperation. We discuss the relationship between our results and the concepts of generalized and indirect reciprocity.


    • Accepted 23 November 2021.
  • Author contributions: research designed by QS and JBP; QS carried out research described in the main text and in SI Annex; BA carried out the research in SI Annex, article 2.3; QS contributed new analysis tools; QS and JBP analyzed the data; and QS and JBP wrote the paper.

  • The authors declare no competing interests.

  • This article is a direct PNAS submission. JJ is a guest editor invited by the Editorial Board.

  • This article contains additional information online at https://www.pnas.org/lookup/suppl/doi:10.1073/pnas.2113468118/-/DCSupplemental.

Data availability

All study data is included in this article and / or SI Annex.

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Shawn Beecher

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